The equation of the piecewise defined function f(x) is below. What is the value of f(1)?

[x²+1, -4 f(x) = -x², 1 3x, x22

f(1) = -2
f(1) = -1
f(1) = 2
f(1) = 3

Answer:5

Step-by-step explanation:

The slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2

An equation is a statement that two expressions are equal. It contains one or more variables and may also contain constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

To find the slope of a line perpendicular to the line whose equation is [tex]2x + 3y = 24[/tex], we need to first find the slope of the given line.

We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:

[tex]2x + 3y = 24[/tex]

[tex]3y = -2x + 24[/tex]

[tex]y = \huge \text(-\dfrac{2}{3}\huge \text )x + 8[/tex]

So the slope of the given line is -2/3.

A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3.

The negative reciprocal of a number is the number flipped upside down and then negated. So the negative reciprocal of -2/3 is:

[tex]-1 \div \huge \text(-\dfrac{2}{3}\huge \text )=\dfrac{3}{2}[/tex]

Therefore, the slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2

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subtract each seperately

first the numbers with x

-2 - -10 becomes -2 + 10 which is 8x

now the constants

then -6 - -2 becomes -6 + 2 which is -4

so its 8x - 4

youre welcome b

Answer:

x = 2;

y = √3

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{y}{1} [/tex]

Cross-multiply to find y:

[tex]y = 1 \times \tan(60°) = 1 \times \sqrt{3} = \sqrt{3} [/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {1}^{2} [/tex]

[tex] {x}^{2} = ( { \sqrt{3}) }^{2} + {1}^{2} = 3 + 1 = 4[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{4} = 2[/tex]

Answer: Let x be the percentage discount given to Scott. Then we can write:

Discounted price for Libby = Original price - 20% of the original price

Discounted price for Scott = Original price - x% of the original price

We know that Libby paid $600 and Scott paid $630 for the same watch, so we can set up the following equation:

Original price - 20% of original price = $600

Original price - x% of original price = $630

Simplifying each equation, we get:

0.8 * Original price = $600

(1 - x/100) * Original price = $630

Dividing the second equation by the first, we get:

(1 - x/100) / 0.8 = 630/600

Simplifying the right-hand side, we get:

(1 - x/100) / 0.8 = 21/20

Multiplying both sides by 0.8, we get:

1 - x/100 = (21/20) * 0.8

Simplifying the right-hand side, we get:

1 - x/100 = 0.84

Subtracting 1 from both sides, we get:

-x/100 = -0.16

Multiplying both sides by -100, we get:

x = 16

Therefore, Scott was given a 16% discount on the original price of the watch.

Step-by-step explanation:

The probability that a record player will break down during the guarantee period is 26.4%.

Cumulative distribution shows the probability of a randomly-selected value falling below or equal to a certain value.

To find the probability that a record player will break down during the guarantee period, we need to calculate the probability of the record player breaking down within two years, which is given by the cumulative distribution function of the normal distribution.

This function uses the mean and standard deviation of the distribution, so for the Radio Shack record player, the probability of breaking down within two years is given by the cumulative distribution function

P(X ≤ 2) = CDF(X; 3.3, 0.8)

To find this probability, we can use a normal distribution calculator to find the cumulative probability of X ≤ 2.

The cumulative probability of X ≤ 2 for a normal distribution with a mean of 3.3 and standard deviation of 0.8 is 2.64.

Therefore, the probability that a Radio Shack record player will break down during the guarantee period is 2.64.

This indicates that there is a 26.4% chance that a Radio Shack record player will break down before the end of the two-year guarantee period.

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sandhyamahilane1116

24.02.2021

Math

Secondary School

answered • expert verified

What is a fraction between 6/7 and 1 whole?

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Given : 6/7 and 1 whole

To Find : a fraction between 6/7 and 1 whole

Solution:

There exist Infinitely many rational between two different rational numbers

There can be Different ways to find rational number in between two number

one way is to find mean of number

= (6/7 + 1)/2

= 13/14

13/14 is a fraction between 6/7 and 1 whole

6/7 = 18/21

1 = 21/21

19/21 , 20/21 are fraction between 6/7 andfraction

Answer:

Perimeter: Add up all the sides (7.5, 6, 2.5, 3.5, 3.5) to get the answer for the perimeter as 23 ft.

Area: Split the shape into two rectangles either way and multiply the length and width. Then, add the two answers. This would leave us with the answer of the area as 35 square feet.

Answer: then get help

Step-by-step explanation:

The value of k in the expression x³ – 6x² – 11x + k is –10.

Polynomial is formed up of the terms Nominal, which means "terms," and Poly, which means "many." A polynomial is a mathematical expression made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

From the question given above, the following data were obtained:

f(x) = x³ – 6x² – 11x + k

Factor => x + 2

Value of k =?

Next, we shall obtained the value of x from x + 2. This can be obtained as follow:

x + 2 = 0

Collect like terms

x = 0 – 2

x = –2

Finally, we shall determine the the value of k. This can be obtained as  illustrated below:

f(x) = x³ – 6x² – 11x + k

x = –2

Value of k =?  

f(–2) = 0 since x + 2 is a factor

x³ – 6x² – 11x + k = 0

(–2)³ – (–2)² – 11(–2) + k = 0

–8 – (4) + 22 + K = 0

–8 – 4 + 22 + K = 0

10 + k = 0

Collect like terms

k = 0 – 10

k = –10

Therefore, the value of k is –10

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The steps to verify the identity cos(-Θ)/(1 + sin(-Θ)) = sec(Θ) + tan(Θ) are:

Start with the left-hand side of the identity: cos(-Θ)/(1 + sin(-Θ))

Use the fact that cos(-Θ) = cos(Θ) and sin(-Θ) = -sin(Θ) to rewrite the expression as: cos(Θ)/(1 - sin(Θ))

Multiply the numerator and denominator by (1 + sin(Θ)) to get: cos(Θ)(1 + sin(Θ))/((1 - sin²(Θ)))

Use the Pythagorean identity sin²(Θ) + cos²(Θ) = 1 to simplify the denominator to cos²(Θ): cos(Θ)(1 + sin(Θ))/(cos²(Θ))

Rewrite the expression using the definitions of secant and tangent: cos(Θ)/cos(Θ) + sin(Θ)/cos(Θ) = sec(Θ) + tan(Θ)

Simplify the expression to arrive at the right-hand side of the identity: sec(Θ) + tan(Θ)

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Image transcribed:

1. Put the steps in order to verify the identity.

cos(-Θ)/1 + sin(-Θ) = sec Θ + tan Θ

↑↓ (cos Θ/1 - sin Θ) (1+ sin Θ/1 + sin Θ)

↑↓ (cos Θ + sin Θ cos Θ) / (1-sin² Ө)

↑↓ cos Θ + sin Θ cos Θ)/ cos² Θ

↑↓ cos Θ/(1- sin Θ)

↑↓ 1/cos Θ + sin Θ/ cos Θ

↑↓ sec Θ +tan Θ

the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues. we first need to calculate the slope (m) and the y-intercept (b)

what do you mean by approximate ?

Approximate means "close to but not exactly" or "an estimate". In other words, an approximate value is a value that is not exact but is close enough to the actual value to be useful or meaningful in a given context.

In the given question,

To find the equation of the line of fit in slope-intercept form, we first need to calculate the slope (m) and the y-intercept (b) using the two given points (8, 12,800) and (14, 14,420).

m = (y₂ - y₁) / (x₂ - x₁)

m = (14,420 - 12,800) / (14 - 8)

m = 1,620 / 6

m = 270

b = y - mx

b = 12,800 - 270(8)

b = 10,940

Therefore, the equation of the line of fit in slope-intercept form is:

y = mx + b

y = 270x + 10,940

To use this equation to estimate the cost of raising a child born in 2013 at age 17, we can plug in x = 17 and solve for y:

y = 270x + 10,940

y = 270(17) + 10,940

y = 15,050

Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues.

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Answer:

x = 4

Step-by-step explanation:

In order to find x, we will either have to find the length QT or RT.

In triangle RST, the length RS is given so we can either length RT or ST. However, if we find the length RT, we can find the value of x.

sin Θ = [tex]\frac{opp}{hyp}[/tex]

sin 60° = [tex]\frac{2\sqrt{3} }{RT}[/tex]

RT = [tex]\frac{2\sqrt{3}}{sin 60}[/tex] = 4

tan Θ = [tex]\frac{opp}{adj}[/tex]

tan 45° = [tex]\frac{x}{4}[/tex]

x = tan 45° × 4 = 4

The indicated side lengths are: x ≈ 13.2 units and y ≈ 11.9 units

the ratio between the side opposite the angle and the hypotenuse of the triangle.

given that a triangle with three sides x, y, 18 and angle opposite to side y is 42°.

then by sine formula, trigonometric ratio for the sine of an angle:

sin(42°) = perpendicular /hypotenuse = y/18

y = 18 sin(42°), we find that y ≈ 11.9 units (rounded to the nearest tenth).

To find x,  the cosine of an angle:

cos(42°) =base /hypotenuse=x/18

x = 18 cos(42°)

we find that x ≈ 13.2 units (rounded to the nearest tenth).

Therefore, the indicated side lengths are:

x ≈ 13.2 units

y ≈ 11.9 units

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Answer:

7 days

Step-by-step explanation:

The textile factory does not have enough dye to dye 5 rolls of fabric using 4 buckets of dye which is certain feet long.

Calculating the amount of dye needed to color one roll of fabric and comparing it to the total amount of dye available will help us decide whether the textile mill can dye 5 rolls of cloth with 4 buckets of dye.

We are aware that a single roll of fabric is 1,067 feet long and need for a 43-liter dye bucket. We divide the dye's volume by the fabric's length to get how much dye is needed per foot of fabric:

0.0403 litres per foot or 43 litres divided by 1,067 feet

Consequently, the factory needs 0.0403 litres of dye to colour one foot of fabric.

Considering there are 4 buckets and each bucket holds 43 litres of colour, the total amount of dye accessible is:

4 buckets at a rate of 43 litres each equal 172 litres.

The factory must dye a total of: to dye 5 rolls of fabric.

5,335 feet are equal to 5 rolls at 1,067 feet each.

We calculate the required amount of dye per foot by the total length of fabric to see if the factory has enough dye to colour this length of fabric:

5,335 feet * 0.0403 litres per foot = 215.1 litres

The manufacturer cannot colour 5 rolls of fabric with 4 buckets of dye because the whole amount of dye needed (215.1 litres) is more than the total amount of dye available (172 litres).

In conclusion, there isn't enough dye in the textile plant to colour 5 rolls of fabric using 4 buckets of dye.

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For given Sample Space, the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5 i.e. A.

What exactly is a sample space?

A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.

Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.

Now,

The probability of a baby being a boy or a girl is 0.5 each, and each birth is an independent event, meaning that the outcome of one birth does not affect the outcome of the others. Therefore, the probability of having 6 girls in a row is (0.5)⁶ = 0.015625, or approximately 1.5625%.

Now, we want to find the probability that the next born child is a boy, given that the first 6 children born were girls.

Using the conditional probability formula:

P(boy | 6 girls) = P(boy and 6 girls) / P(6 girls)

The probability of having 6 girls and a boy is the same as the probability of having 7 children in a row, with the last one being a boy. The probability of having 7 children in a row, with any gender, is (0.5)⁷ = 0.0078125, or approximately 0.78125%.

Therefore,

P(boy | 6 girls) = (0.5)⁷ / (0.5)⁶ = 0.5

So the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5.

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Answer:

x = 25

Step-by-step explanation:

By the angle sum property,

2x + 2 + 5x + 3 = 180

7x + 5 = 180

7x = 175

x = 25

Pls like and mark as brainliest!

Answer:

x = 25

Step-by-step explanation:

2x + 2 + 5x + 3 = 180

7x + 5 = 180 and 7x=175

7x = 175

x = 25

so x is most  likely the answer

x=25 Give her BRAINLEST for figuring it out first

Answer: We can determine which graph represents which polynomial function by analyzing the factors of each function.

First, let's consider f(x) = (x + 3)(x + 4). The factors are (x + 3) and (x + 4). When we multiply these factors together, we get a quadratic polynomial with a positive leading coefficient. This means that the graph of f(x) will be a parabola that opens upward.

Next, let's consider g(x) = 1/3(x + 3)(x − 4). The factors are (x + 3) and (x - 4). When we multiply these factors together and simplify, we get a quadratic polynomial with a leading coefficient of 1/3. This means that the graph of g(x) will also be a parabola that opens upward, but it will be narrower than the graph of f(x).

Based on this analysis, we can determine that the graph of f(x) corresponds to the wider parabola, and the graph of g(x) corresponds to the narrower parabola. We can also determine this without using graphing software by noting that f(x) has roots at x = -3 and x = -4, while g(x) has roots at x = -3 and x = 4. The graph of f(x) must therefore intersect the x-axis at -3 and -4, while the graph of g(x) must intersect the x-axis at -3 and 4. By examining the graphs, we can see that the wider parabola intersects the x-axis at -3 and -4, so it corresponds to f(x), while the narrower parabola intersects the x-axis at -3 and 4, so it corresponds to g(x).

Step-by-step explanation:

A boat's distance from the coast is measured from station A, where the angle is [tex]50[/tex] degrees, and the shore lies [tex]868[/tex] feet away.

A scalar number known as distance measures "how so much ground an item has traversed" while moving. A vector quantity called displacement describes how far an item is out of place.

A segment's or a room's dimensions are examples of things that may be measured in terms of length. Distance is the separation between two things, like two major cities or 2 points. There will never be a zero sign for either length or distance.

Let Ø be the third angle in the triangle.  Ø=180°-70°-60°=180°-130°=50°

Since we now have an angle and its opposite side, the Law of Sines can be used to find the lengths of other sides.  Let [tex]X[/tex] be the distance from the boat to station A, then

590/sin(Ø)=X/sin(°70)

X=590[sin(70°)/sin(50°)]=868 ft

Distance boat to shore=868sin(70°)[tex]=868 ft[/tex]

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The least possible number of games that Jennifer won is three. This is because when the total number of games won is 300.

A situation where two or more decisions makers (players) have to make decisions based on the probabilities of each outcome.

To find this number, we must first calculate the total number of games played. Since Jennifer won 30%, Grace won 25%, and Janet won 45%, the total number of games played can be determined by multiplying the total percentage by the number of players.

30% + 25% + 45% = 100%

100%  x  3 players = 300 games played

To find out how many games Jennifer won, we must multiply 30% by the total number of games played.

30% x 300 games = 90 games

Since Jennifer won 90 games, Grace won 25% of 300 games, which is 75 games, and Janet won 45% of 300 games, which is 135 games, the total number of games won is 300.

Therefore, the least possible number of games that Jennifer won is three. This is because when the total number of games won is 300, the least possible number of games that one player can win is three.

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To compute the CPI, we first need to calculate the total cost of the basket in both years:

2017: (10 x $40) + (30 x $10) = $400 + $300 = $700

2018: (12 x $60) + (50 x $12) = $720 + $600 = $1320

Using 2017 as the base year, the CPI in 2017 is 100 (by definition). To calculate the CPI in 2018, we divide the cost of the basket in 2018 by the cost of the basket in 2017, and multiply by 100:

CPI in 2018 = (1320/700) x 100 = 188.57

Therefore, the percentage change in the overall price level is:

% change in price level = (CPI in 2018 - CPI in 2017) / CPI in 2017 x 100

% change in price level = (188.57 - 100) / 100 x 100

% change in price level = 88.57%

So, the overall price level increased by 88.57% from 2017 to 2018.

Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:

h(t) = -12t^2 + 20t + 30

where t is the time in seconds since the ball was thrown.

To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.

Therefore, we can substitute t = 0 into the expression for h(t):

h(0) = -12(0)^2 + 20(0) + 30 = 30

This means that the balcony is 30 feet above the ground.

Hence, the height of the balcony above the ground is 30 feet.

Step-by-step explanation:

Answer:

Step-by-step explanation:Let's first substitute the values of A, P, and T in the formula A = P(1 + r)^T.

Given: A = 1,000,000; P = 10,000; T = 2

1,000,000 = 10,000(1 + r)^2

Now let's express it as a quadratic equation. First, divide both sides by 10,000:

100 = (1 + r)^2

Next, expand the square:

100 = 1 + 2r + r^2

Finally, rearrange to form the quadratic equation:

r^2 + 2r - 99 = 0

To represent the formula A = P(1 + r) as a quadratic equation with the given values, we substitute A = 1,000,000, P = 10,000, and T = 2. The resulting equation is 10,000r - 9,000,000 = 0.

To express the formula A = P(1 + r) as a quadratic equation, we substitute the given values for A, P, and T.

Given:

Substituting these values into the formula:

1,000,000 = 10,000(1 + r)

To express this equation as a quadratic form, we can expand the parentheses:

1,000,000 = 10,000 + 10,000r

Now, let's move all the terms to one side to form a quadratic equation:

10,000r - 9,000,000 = 0

Therefore, the quadratic equation that represents A = P(1 + r) with the given values is 10,000r - 9,000,000 = 0.

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The simplified form of the function f(x)=1/2(27) 2x/3 can be expressed as f(x) = (27/2) (2x/3).

Functions are one of the fundamental building blocks of mathematics and are used to describe and analyze relationships between different variables.

The function f(x)=1/2(27) 2x/3 can be simplified by factoring out the common factor of 1/2 and 27.

Thus, the simplified form of the function can be expressed as

f(x) = (27/2) (2x/3).

This function is a polynomial function with degree 1, which means that it is a linear function. The degree of a function is the highest power of the variable in the equation.

The key aspects of this function can be identified by looking at the constant values in the equation.

The constant value 27/2 is the y-intercept, which is the point at which the line crosses the y-axis.

This means that the y-value of the function at x = 0 is 27/2.

The constant value 2/3 is the gradient, which is the slope of the line. This means that for every increase in the x-value, the y-value will increase by 2/3.

This function can be represented graphically as a straight line with a y-intercept of 27/2 and a slope of 2/3.

The graph of this function will pass through the point (0, 27/2) and will have a positive slope of 2/3. This means that the graph will move up and to the right, with each increase in the x-value resulting in an increase of 2/3 in the y-value.

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Answer: 9cm

Step-by-step explanation: i hope this this helps!

Answer:

It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.

Answer:

y = 2;

x = 2√2

.

Step-by-step explanation:

Use trigonometry:

[tex] \tan(45°) = \frac{y}{2} [/tex]

Use the property of proportion to find x (cross-multiply):

[tex]y = 2 \times \tan(45°) = 2 \times 1 = 2[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {2}^{2} [/tex]

[tex] {x}^{2} = {2}^{2} + {2}^{2} = 4 + 4 = 8[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} [/tex]

The length of the parking lot in the drawing is 44 centimeters.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

Since the scale Colton used is 1 centimeter : 2 meters, this means that for every 2 meters in real life, he drew 1 centimeter in his scale drawing.

To find the length of the parking lot in the drawing, we can set up a proportion:

1 cm / 2 m = x cm / 88 m

where x is the length of the parking lot in the drawing in centimeters.

We can solve for x by cross-multiplying:

1 cm * 88 m = 2 m * x cm

88 cm = 2x

x = 44 cm

Therefore, the length of the parking lot in the drawing is 44 centimeters.

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